Ratio and Proportion

Question 1

What is a ratio?

Answer 1

A ratio is a relationship between two or more quantities showing the number of times one is contained within the other(s)

Ratios are written in a:b / a:b:c form

They can be represented as a draction too a/b

Ratios can be used in a variety of ways;

Working out,
Simplifying
Dividing
Ratio -> Fractions
Problem Solving
Scaled

Question 2

What is a proportion?

Answer 2

Proportion is a type of relationship between two variables linked by a constant.

There are two types, direct and inverse.

The symbol ‘∝’ means ‘is proportional to’.

if y is directly proportional to x we can write it as y ∝ x

Which the formula is y = kx

if it is inverse it it written as
y = k/x

Question 3

If x is directly proportional to y then what is y if x equals 3?

x = 1
y = 60

Answer 3

x = 1
y = 60

x = 3
y = 180

y*x

Question 4

If x is inverse proportional to y then what is y if x equals 3?

x = 1
y = 30

Answer 4

x = 1
y = 30

x = 3
y = 10

y = 30/3

You take the original value which is 30 and divide it by the x so it is 30/3

Question 5

Solving ratio and proportion problems.

Answer 5

Sometimes a proportion problem may also involve ratios.

a café sells apples and bananas in the ratio 2:3. They sell 35 pieces of fruit altogether apples cost 30p and bananas cost 45p. Work out the total amount of money the fruit cost.

So, first you use the ratio to work out how many apples and bananas were sold. The ratio 2:3 has 5 parts (2+3) so you divide 35 by 5 to get 7. Then you multiply each part of the ratio by 7 that means that 14 apples and 21 bananas were sold.

2:3

27:37
14:21

Apples: 1430 = 420
Bananas: 2145 = 945

420+945=1365

Total price is $13.65

Question 6

what is the formula for inverse proportion?

Answer 6

y = k/x

Question 7

what is the formula for proportion

Answer 7

y = kx

Question 8

Simon made a scale model of a car on a scale of 1 to 12.5 . The height of the model car is 10cm.

Work out the height of the real car.

Answer 8

The ratio of the lengths is 1 : 12.5 .

So for every 1 unit of length the small car is, the real car is 12.5 units. So if the small car is 10 units long, the real car is 125 units long. If the small car is 10cm high, the real car is 125cm high.

We know that model : real = 1 : 12.5 . However, the real car is 500cm, so 1 : 12.5 = x : 500 (the ratios have to remain the same). x is the length of the model car.

To work out the answer, we convert the ratios into fractions:

1 = x

12.5 500

multiply both sides by 500:

500/12.5 = x

so x = 40cm

Question 9

Simplifying ratios.

Answer 9

Ratios can fully be fully simplified just like fractions, to simplify a ratio divide all the numbers in the ratio by the same number until they cannot be divided anymore.

simplify 6:12

6:12 = 3:6
3:6 = 1:2

Question 10

Simplify 4:6

Answer 10

2:3

Question 11

Simplify 9:12

Answer 11

3:4

Question 12

Simplify 5:10:15

Answer 12

1:2:3

Question 13

Finding unknown ratios.

Answer 13

Some boys and girls are divided into teams in the ratio 3:4 there are 8 girls in one team. How many boys are there in the team?

There are 8 girls shared into 4 parts. Each part has 8/4 = 2 girls.

Boys: 2-2-2 (3:x)
Girls: 2-2-2-2 (x:4)

From the diagram it is clear the number of boys in the team is 2x3=6

Question 14

Sweets and chocolate are divided into trays in the ratio 2:6 there are 12 chocolates in one tray how many sweets are there?

Answer 14

there are 12 chocolates shared into 6 parts. 12/6 = 2 Chocolates

Sweets: 2-2
Chocolate: 2-2-2-2-2-2

From the diagram it is clear there are 4 sweets.